arXiv subjects

Thomas März

Publications and source records attributed to Thomas März.

At least 19 recordsLinked to original sources

arXiv2026

MPISuperRes-PnP: A Super-Resolution Zero-Shot Plug-and-Play Reconstruction Algorithm for Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is an emerging medical imaging modality. MPI is based on the non-linear response of magnetic nanoparticles to an applied magnetic field and avoids ionizing radiation. The measured signal is the voltage induced in receive coils by the particles' response. Reconstructing the particle concentration from the signal constitutes the imaging task. Even using state-of-the-art measurement-based reconstruction, the associated spatial grid is very coarse, hence super-resolution (SR) techniques are important. In this work, we propose an approach for SR in MPI inspired by energy minimization. Different methods have been proposed for SR in MPI, ranging from upscaling of the associated system matrix to interpolation of the reconstruction. Here we incorporate SR into the reconstruction task via an energy minimization formulation. Following the plug-and-play approach to energy minimization we derive a splitting scheme and a SR method for MPI where the arising Gaussian denoising task is treated with a pre-trained learned Gaussian denoiser in a zero-shot fashion. This way, we incorporate benefits of deep learning without training and avoid the need of training data. Further, we provide a quantitative and qualitative evaluation of the proposed method. Hyper-parameter are selected via an extended parameter search. The found parameters are applied for reconstruction on real data. We show the applicability of our method on synthetic and on real data (MPIData: EquilibriumModelWithAnisotropy and 2D-OpenMPI Data). The proposed method employs a deep-learning denoiser without training -- thus it does not require presently scarcely available MPI training data. The denoiser behaves conservatively, i.e., no hallucination artifacts were observed. The SR approach is generic such that it can be applied in future MPI contexts involving different regularizers or different imaging tasks.

cs.CV↗

arXiv2026

Flood Mapping from RGB imagery using a Vision Foundation Model

Timely, high-resolution maps of flood extent around settlements are essential for emergency response and damage assessment. We consider airborne RGB imagery for flood mapping as it can be collected rapidly at low cost. To produce flood maps, deep learning models for water segmentation are often used. CNN based and small vision transformer models are used. However, they need much data for adaptation to a change of scenery, i.e., another flooding event. Vision foundation models or large vision transformers are known to generalize across domains. Recently, foundation models for Earth observation became available. They are pretrained on satellite data, whose spatial resolution, viewing geometry, and radiometry differ from nadir RGB imagery. Thus, adaptation is required. We investigate how a satellite-pretrained Earth observation foundation model can be adapted to centimeter-scale floodwater mapping from RGB imagery. Specifically, we fine-tune a model we call Prithvi-2.0-UPN consisting of the Prithvi-EO-2.0-600M Vision Transformer combined with a UPerNet decoder for binary water segmentation on two RGB datasets (BlessemFlood21, NeuenahrFlood). In a first experiment we observe that Prithvi-2.0-UPN reaches state-of-the-art results on BlessemFlood21 and NeuenahrFlood, when trained on their datasets. In a second experiment we show that Prithvi-2.0-UPN performs better than state-of-the-art baseline models for transfer to a new flood event (trained on BlessemFlood21, tested on NeuenahrFlood) in a zero-shot setting. However, the performance indicates room for improvement. In this respect, we investigate in a third experiment how performance improves when further fine-tuning the models with small shares of NeuenahrFlood training data: Prithvi-2.0-UPN improves the fastest and reaches almost the performance level when fully trained on NeuenahrFlood, indicating transfer capabilities.

cs.CV↗

arXiv2026

Debye Relaxation in Model-Based Multi-Dimensional Magnetic Particle Imaging

Model-based reconstruction approaches for the medical imaging modality Magnetic Particle Imaging (MPI) are typically based on the Langevin model, which assumes instantaneous alignment of the particles magnetic momenta with the applied field. Regarding the application to real data, Langevin model-based reconstruction methods require model transfer functions (MTF) obtained from calibrations to preprocess the data. There are also model-based reconstruction approaches that include relaxation effects and other particle-level dynamics. However, they are limited either to 1D or 1D-like scanning scenarios when considering real data, or are limited to simulated data in the case of multi-dimensional field-free point (FFP) MPI. Thus, fully model-based reconstructions from multi-dimensional FFP scanning data that incorporate relaxation effects without using an MTF have not yet been demonstrated. In this work, we incorporate relaxation effects by considering a multi-dimensional Debye model and provide reconstruction formulae. In particular, we show that the Debye model-based signal is the response of a linear time-invariant system with exponential memory applied to a Langevin model-based signal. We provide a reconstruction algorithm for the introduced multi-dimensional Debye model. To this end, we devise a relaxation adaption step. For the resulting relaxation-adapted Debye signal, we show that it can be expressed by the well-studied MPI core operator derived from the Langevin theory. This results in a three-stage algorithm with low additional cost over the Langevin model, as the relaxation adaption scales linearly in the input data. We provide numerical results for the proposed algorithmic approach. In particular, we obtain fully model-based reconstructions from real 2D MPI data without involving any specific MTF analogous to the Langevin model case.

math.NA↗

arXiv2025

Higher Order Regularization using Harmonic Eigenfunctions for Model-Based Reconstruction in Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the particles. Generally, in computational imaging variational reconstruction techniques are common and rely on a mathematical model to describe the underlying physics. For the MPI reconstruction task we propose a model-based variational reconstruction technique which incorporates a higher order regularizer, where the regularizer is diagonalized by harmonic eigenfunctions. The proposed image reconstruction algorithm features two major stages: in the first stage, the core stage, the components of the MPI core response are reconstructed. This is the MPI-specific data approximation task which we formulate as a variational problem incorporating the higher order regularizer. The relationship between the particle distribution, the MPI core response and the measured data is given by a mathematical model which was introduced in our earlier research. According to this model the MPI core response is tied to the particle distribution by convolution. Therefore the outcome of the core stage yields the data for the second stage, the deconvolution stage, in which the final reconstructed image is produced by solving an ill-posed deconvolution problem in a robust way relying on earlier research. Interestingly, the quality of the final image depends significantly on the quality of the result of the core stage. A contribution is thus the enhancement of the core stage via higher order regularization. We provide a theoretical foundation for our approach and demonstrate its benefit with numerical examples.

math.NA↗

arXiv2025

Reconstruction Formulae for 3D Field-Free Line Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exposing them to dynamic magnetic fields. In the Field-Free Line (FFL) scanner topology, the spatial encoding of the particle distribution is performed by applying magnetic fields vanishing on straight lines. The voltage induced in the receiving coils by the particles when exposed to the magnetic fields constitute the signal from which the particle distribution is to be reconstructed. To avoid lengthy calibration, model-based reconstruction formulae have been developed for the 2D FFL scanning topology. In this work we develop reconstruction formulae for 3D FFL. Moreover, we provide a model-based reconstruction algorithm for 3D FFL and we validate it with a numerical experiment.

math.NA↗

arXiv2025

Fast Trajectory-Independent Model-Based Reconstruction Algorithm for Multi-Dimensional Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a promising tomographic technique for visualizing the spatio-temporal distribution of superparamagnetic nanoparticles, with applications ranging from cancer detection to real-time cardiovascular monitoring. Traditional MPI reconstruction relies on either time-consuming calibration (measured system matrix) or model-based simulation of the forward operator. Recent developments have shown the applicability of Chebyshev polynomials to multi-dimensional Lissajous Field-Free Point (FFP) scans. This method is bound to the particular choice of sinusoidal scanning trajectories. In this paper, we present the first reconstruction on real 2D MPI data with a trajectory-independent model-based MPI reconstruction algorithm. We further develop the zero-shot Plug-and-Play (PnP) algorithm of the authors -- with automatic noise level estimation -- to address the present deconvolution problem, leveraging a state-of-the-art denoiser trained on natural images without retraining on MPI-specific data. We evaluate our method on the publicly available 2D FFP MPI dataset ``MPIdata: Equilibrium Model with Anisotropy", featuring scans of six phantoms acquired using a Bruker preclinical scanner. Moreover, we show reconstruction performed on custom data on a 2D scanner with additional high-frequency excitation field and partial data. Our results demonstrate strong reconstruction capabilities across different scanning scenarios -- setting a precedent for general-purpose, flexible model-based MPI reconstruction.

cs.CV↗

arXiv2025

Remote Sensing Imagery for Flood Detection: Exploration of Augmentation Strategies

Floods cause serious problems around the world. Responding quickly and effectively requires accurate and timely information about the affected areas. The effective use of Remote Sensing images for accurate flood detection requires specific detection methods. Typically, Deep Neural Networks are employed, which are trained on specific datasets. For the purpose of river flood detection in RGB imagery, we use the BlessemFlood21 dataset. We here explore the use of different augmentation strategies, ranging from basic approaches to more complex techniques, including optical distortion. By identifying effective strategies, we aim to refine the training process of state-of-the-art Deep Learning segmentation networks.

cs.CV↗

arXiv2025

An $\ell^1$-Plug-and-Play Approach for MPI Using a Zero Shot Denoiser with Evaluation on the 3D Open MPI Dataset

Objective: Magnetic particle imaging (MPI) is an emerging medical imaging modality which has gained increasing interest in recent years. Among the benefits of MPI are its high temporal resolution, and that the technique does not expose the specimen to any kind of ionizing radiation. It is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. From the electric signal measured in receive coils, the particle concentration has to be reconstructed. Due to the ill-posedness of the reconstruction problem, various regularization methods have been proposed for reconstruction ranging from early stopping methods, via classical Tikhonov regularization and iterative methods to modern machine learning approaches. In this work, we contribute to the latter class: we propose a plug-and-play approach based on a generic zero-shot denoiser with an $\ell^1$-prior. Approach: We validate the reconstruction parameters of the method on a hybrid dataset and compare it with the baseline Tikhonov, DIP and the previous PP-MPI, which is a plug-and-play method with denoiser trained on MPI-friendly data. Main results: We offer a quantitative and qualitative evaluation of the zero-shot plug-and-play approach on the 3D Open MPI dataset. Moreover, we show the quality of the approach with different levels of preprocessing of the data. Significance: The proposed method employs a zero-shot denoiser which has not been trained for the MPI task and therefore saves the cost for training. Moreover, it offers a method that can be potentially applied in future MPI contexts.

eess.IV↗

arXiv2025

Enhanced Low-Dose CT Image Reconstruction by Domain and Task Shifting Gaussian Denoisers

Computed tomography from a low radiation dose (LDCT) is challenging due to high noise in the projection data. Popular approaches for LDCT image reconstruction are two-stage methods, typically consisting of the filtered backprojection (FBP) algorithm followed by a neural network for LDCT image enhancement. Two-stage methods are attractive for their simplicity and potential for computational efficiency, typically requiring only a single FBP and a neural network forward pass for inference. However, the best reconstruction quality is currently achieved by unrolled iterative methods (Learned Primal-Dual and ItNet), which are more complex and thus have a higher computational cost for training and inference. We propose a method combining the simplicity and efficiency of two-stage methods with state-of-the-art reconstruction quality. Our strategy utilizes a neural network pretrained for Gaussian noise removal from natural grayscale images, fine-tuned for LDCT image enhancement. We call this method FBP-DTSGD (Domain and Task Shifted Gaussian Denoisers) as the fine-tuning is a task shift from Gaussian denoising to enhancing LDCT images and a domain shift from natural grayscale to LDCT images. An ablation study with three different pretrained Gaussian denoisers indicates that the performance of FBP-DTSGD does not depend on a specific denoising architecture, suggesting future advancements in Gaussian denoising could benefit the method. The study also shows that pretraining on natural images enhances LDCT reconstruction quality, especially with limited training data. Notably, pretraining involves no additional cost, as existing pretrained models are used. The proposed method currently holds the top mean position in the LoDoPaB-CT challenge.

eess.IV↗

arXiv2024

BlessemFlood21: Advancing Flood Analysis with a High-Resolution Georeferenced Dataset for Humanitarian Aid Support

Floods are an increasingly common global threat, causing emergencies and severe damage to infrastructure. During crises, organisations such as the World Food Programme use remotely sensed imagery, typically obtained through drones, for rapid situational analysis to plan life-saving actions. Computer Vision tools are needed to support task force experts on-site in the evaluation of the imagery to improve their efficiency and to allocate resources strategically. We introduce the BlessemFlood21 dataset to stimulate research on efficient flood detection tools. The imagery was acquired during the 2021 Erftstadt-Blessem flooding event and consists of high-resolution and georeferenced RGB-NIR images. In the resulting RGB dataset, the images are supplemented with detailed water masks, obtained via a semi-supervised human-in-the-loop technique, where in particular the NIR information is leveraged to classify pixels as either water or non-water. We evaluate our dataset by training and testing established Deep Learning models for semantic segmentation. With BlessemFlood21 we provide labeled high-resolution RGB data and a baseline for further development of algorithmic solutions tailored to flood detection in RGB imagery.

cs.CV↗

arXiv2024

Variational Model-Based Reconstruction Techniques for Multi-Patch Data in Magnetic Particle Imaging

Magnetic Particle Imaging is an emerging imaging modality through which it is possible to detect tracers containing superparamagnetic nanoparticles. The exposure of the particles to dynamic magnetic fields generates a non-linear response that is used to locate the particles and produce an image of their distribution. The bounding box that can be covered by a single scan curve depends on the strength of the gradients of the magnetic fields applied, which is limited due to the risk of causing peripheral nerve stimulation (PNS) in the patients. To address this issue, multiple scans are performed. The scan data must be merged together to produce reconstructions of larger regions of interest. In this paper we propose a mathematical framework which can deal with rather general multi-patching scenarios including rigid transformations of the field of view (FoV), the specimen and of the scanner. We show the flexibility of this framework in a variety of different scanning scenarios. Moreover, we describe an iterative reconstruction algorithm that yields a reconstruction of the target distribution by minimizing a convex functional which includes positivity constraints and sparsity enforcing priors. We show its convergence to a minimizer and perform numerical experiments on simulated data.

math.NA↗

arXiv2017

Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

math.NA↗

arXiv2016

Model-Based Reconstruction for Magnetic Particle Imaging in 2D and 3D

We contribute to the mathematical modeling and analysis of magnetic particle imaging which is a promising new in-vivo imaging modality. Concerning modeling, we develop a structured decomposition of the imaging process and extract its core part which we reveal to be common to all previous contributions in this context. The central contribution of this paper is the development of reconstruction formulae for MPI in 2D and 3D. Until now, in the multivariate setup, only time consuming measurement approaches are available, whereas reconstruction formulae are only available in 1D. The 2D and the 3D (describing the real world) reconstruction formulae which we derive here are significantly different from the 1D situation -- in particular there is no Dirac property in dimensions greater than one when the particle sizes approach zero. As a further result of our analysis, we conclude that the reconstruction problem in MPI is severely ill-posed. Finally, we obtain a model-based reconstruction algorithm.

math.NA↗

arXiv2014

Anisotropic Diffusion on Curved Surfaces

We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence enhancing diffusion models in a surface-intrinsic way. These diffusion processes are anisotropic and the equations depend non-linearly on the data. The surface-intrinsic equations are dealt with the closest point method, a technique for solving partial differential equations (PDEs) on general surfaces. The resulting algorithm has a very simple structure: we merely alternate a time step of a 3D analog of the in-surface PDE in a narrow 3D band containing the surface with a reconstruction of the surface function. Surfaces are represented by a closest point function. This representation is flexible and the method can treat very general surfaces. Experimental results include image filtering on smooth surfaces, open surfaces, and general triangulated surfaces.

math.NA↗

arXiv2013

An embedded method-of-lines approach to solving partial differential equations on surfaces

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the surface in a band containing the surface. We define a modified equation in the band, obtained in a straightforward way from the original evolution PDE, and show that the solutions of this equation are consistent with those of the surface equation. The resulting system can then be solved with standard implicit or explicit time-stepping schemes, and the solutions in the band can be restricted to the surface. Our derivation generalizes existing formulations of the closest point method and is amenable to standard convergence analysis.

math.NA↗

arXiv2012

An Embedding Technique for the Solution of Reaction-Diffusion Equations on Algebraic Surfaces with Isolated Singularities

In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singularity. In our approach, we first desingularize the curve by appealing to techniques from algebraic geometry. We create a family of smooth curves in higher dimensional space that correspond to the original curve by projection. Following this, we pose the analogous reaction-diffusion PDE on each member of this family and show that the solutions (their projection onto the original domain) approximate the solution of the original problem. Finally, we compute these approximants numerically by applying the Closest Point Method which is an embedding technique for solving PDEs on smooth surfaces of arbitrary dimension or codimension, and is thus suitable for our situation. In addition, we discuss the potential to generalize the techniques presented for higher-dimensional surfaces with multiple singularities.

math.NA↗

arXiv2012

Calculus on Surfaces with General Closest Point Functions

The Closest Point Method for solving partial differential equations (PDEs) posed on surfaces was recently introduced by Ruuth and Merriman [J. Comput. Phys. 2008] and successfully applied to a variety of surface PDEs. In this paper we study the theoretical foundations of this method. The main idea is that surface differentials of a surface function can be replaced with Cartesian differentials of its closest point extension, i.e., its composition with a closest point function. We introduce a general class of these closest point functions (a subset of differentiable retractions), show that these are exactly the functions necessary to satisfy the above idea, and give a geometric characterization of this class. Finally, we construct some closest point functions and demonstrate their effectiveness numerically on surface PDEs.

math.NA↗

arXiv2010

Image Inpainting Based On Coherence Transport With Adapted Distance Functions

We discuss an extension of our method Image Inpainting Based on Coherence Transport. For the latter method the pixels of the inpainting domain have to be serialized into an ordered list. Up till now, to induce the serialization we have used the distance to boundary map. But there are inpainting problems where the distance to boundary serialization causes unsatisfactory inpainting results. In the present work we demonstrate cases where we can resolve the difficulties by employing other distance functions which better suit the problem at hand.

math.NA↗